Kinematics of a 2D Asymmetric Nonlinear Oscillator

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Abstract

Motion of a point-like massive particle under the influence of two nonidentical linear springs
conducive to an irregular planar oscillation is analyzed. For a two dimensional oscillations the
equation of motion is a coupled highly nonlinear differential equation. The set of equations cannot
be solved analytically. Utilizing a Computer Algebra System (CAS) such as Mathematica [1] we
solve the equations numerically. Kinematics of the particle is presented. For a comprehensive
visual understanding the oscillations are simulated. We also include an extended atlas of useful
two-dimensional time-folded diagrams